Enceladus, a tiny moon of Saturn, is found to be geologically active. In 2005, Cassini detected an anomalously warm region and a plume, consisting of mostly water vapor and ice grains, at its south pole. The plume has far-reaching effects on the Saturnian system and offers clues into the moon’s interior, particularly as to whether liquid water exists underground. Consequently, understanding the physics and source conditions of the plume is crucial, which is the focus of this work. The plume is not only two-phase but also multi-regime in nature and can be divided into three distinct regions: a subsurface region, a collisional near-field and a free-molecular far-field. To study it, a hybrid model of the plume, which treats each region separately, is constructed. Two subsurface models are considered. Using the resulting vent conditions from these models, the plume is propagated from the surface vents out to several Enceladus radii using the direct simulation Monte Carlo (DSMC) method in the near-field and a free-molecular model in the far-field. The model is used to examine the plume flow, with and without grains. Collisions are found to be important in various processes, including grain condensation and flow acceleration. Since collision rates drop away from the vent, they must be high enough at the vent to enable significant condensation to occur and the gas to accelerate to the maximum speed possible by allowing energy stored in internal modes to be converted into translational energy as the gas expands. When slower grains are present, however, they may decelerate and push the gas out more laterally. Moreover, grains may form a thick column and restrict the free expansion of the gas. Smaller grains have greater and more extensive effects on the gas, but are also more strongly affected by the gas. Their motions decouple from the gas motions higher above the vent. They are also more likely to spread with the gas and be accelerated to the gas speeds. By constraining the plume far-field using Cassini data, the H2O and grain production rates from the plume are estimated to be ~100–1000 kg/s and < 10 kg/s respectively, which agree with other estimates. Based on fit results, the gas jets appear to be narrow, suggesting high Mach numbers at the vents. / text

The thesis considers two distinct strategies for algebraic computation with polynomials in high dimension. The first concerns ideals and varieties with symmetry, which often arise in applications from areas such as algebraic statistics and optimization. We explore the commutative algebra properties of such objects, and work towards classifying when symmetric ideals admit finite descriptions including equivariant Gröbner bases and generating sets. Several algorithms are given for computing such descriptions. Specific focus is given to the case of symmetric toric ideals. A second area of research is on problems in numerical algebraic geometry. Numerical algorithms such as homotopy continuation can efficiently compute the approximate solutions of systems of polynomials, but generally have trouble with multiplicity. We develop techniques to compute local information about the scheme structure of an ideal at approximate zeros. This is used to create a hybrid numeric-symbolic algorithm for computing a primary decomposition of the ideal.

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We present a series of numerical galaxy formation studies which apply new numerical methods to produce increasingly realistic galaxy formation models. We first investigate the metallicity evolution of a large set of idealized hydrodynamical galaxy merger simulations of colliding galaxies. We find that inflows of metal--poor interstellar gas triggered by galaxy tidal interactions can account for the systematically lower central oxygen abundances observed in local interacting galaxies. We show the central metallicity evolution during merger events is determined by a competition between the inflow of low--metallicity gas and enrichment from star formation. We find a time-averaged depression in the galactic nuclear metallicity of ~0.07 dex for gas--poor disk--disk interactions, which explains the observed close pair mass-metallicity and separation-metallicity relationships. / Astronomy

Recent work by a number of researchers has highlighted areas in which conservative numerical methods give poor solutions. One such situation is in the modelling of material interfaces. A number of methods for overcoming this shortfall of conservative numerical methods are developed. The flow situations that are considered include multicomponent gases and systems of gases and liquids. It is shown that the errors associated with conservative methods when applied to model gas-liquid interfaces are considerably larger than those for gas-gas interfaces. The first approach used for overcoming the errors in conservative methods is a hybrid primitive-conservative method. This method is used in conjunction with a number of new Riemann solvers for a liquid ambient to provide accurate solutions to a number of challenging one and two dimensional test problems. These test problems include the interaction of a shock wave with a bubble in a gas and an underwater explo.; ion. The application of these hybrid methods to the problem of the interaction of a shock wave with a gas bubble in aa liquid demonstrate that they are unable to provide an accurate solution. Two one dimensional methods are described that are able to provide solutions to such test problems. These methods are the moving grid-Chimera approach and a cut cell approach. The cut cell approach is extended into two dimensions and is shown to be able to provide solutions to the problem of the interaction of a shock wave with a gas bubble in a liquid. This method is also shown to be able to provide more accurate solutions to multicomponent gas problems than those on a standard Cartesian grid.

This thesis presents a detailed study of the numerical errors and the associated accuracy-efficiency tradeoffs encountered in the solution of frequency- and time-domain integral equations. For frequency-domain integral equations, the potential integrals contain singular Green’s function kernels and the resulting singular and near-singular integrals must be carefully evaluated, using singularity extraction or cancellation techniques, to ensure the accuracy of the method-of-moments impedance matrix elements. This thesis presents a practical approach based on the progressive Gauss-Patterson quadrature rules for implementing the radial-angular-transform singularity-cancellation method such that all singular and near-singular integrals are evaluated to an arbitrary pre-specified accuracy. Numerical results for various scattering problems in the high- and low-frequency regimes are presented to quantify the efficiency of the method and contrast it to the singularity extraction method. For time-domain integral equations, the singular Green’s function kernels are functions of space and time and sub-domain temporal basis functions rather than entire-domain sinusoidal/Fourier basis functions are used to represent the time variation of currents/fields. This thesis also investigates the accuracy-efficiency tradeoff encountered when choosing sub-domain temporal basis functions by contrasting two prototypical ones: The causal piecewise polynomial interpolatory functions, sometimes called shifted Lagrange interpolants, and the band-limited interpolatory functions based on approximate prolate spheroidal wave functions. It is observed that the former is more efficient for low to moderate accuracy levels and the latter achieves higher, but extrapolation-limited, accuracy levels. / text

published_or_final_version / abstract / toc / Computer Science and Information Systems / Master / Master of Philosophy

published_or_final_version / abstract / toc / Mechanical Engineering / Master / Master of Philosophy

published_or_final_version / abstract / toc / Mathematics / Master / Master of Philosophy

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy